Atoms · 3 min read
Atomic Number (Z) · Isotopes
The atomic number equals the number of protons in the nucleus and defines the element's identity. All atoms of a given element have the same atomic number: carbon always has 6 protons and oxygen always has 8. Changing the atomic number changes the element. In a neutral atom, the number of electrons equals the number of protons. Ions form when atoms gain or lose electrons: cations are positive (fewer electrons than protons) and anions are negative (more electrons than protons).
Mass Number (A)
A = Z + (number of neutrons) number of neutrons = A − Z
electrons in an ion = Z − (ion charge)
A is always a whole number (a count of nucleons). Carbon-12 has Z = 6 and A = 12, so it has 12 − 6 = 6 neutrons. ⁵⁶Fe³⁺ has 26 protons, 30 neutrons, and 26 − 3 = 23 electrons.
Atomic Mass
Atomic mass (atomic weight) is the weighted average mass of all naturally occurring isotopes of an element. It is the value on the periodic table, expressed in amu (or g/mol for one mole of atoms). The average lies closest to the mass of the most abundant isotope.
Atomic mass = Σ (isotope mass × fractional abundance)
Convert percent abundances to fractions (75.77% → 0.7577); the fractions must sum to 1.
Chlorine: Cl-35 (34.97 amu, 75.77%) and Cl-37 (36.97 amu, 24.23%)
Atomic mass = (34.97)(0.7577) + (36.97)(0.2423)
= 26.50 + 8.958 = 35.45 amu
Reverse problem: Cu = 63.55 amu; Cu-63 = 62.93 amu, Cu-65 = 64.93 amu
Let x = fraction of Cu-63: 62.93x + 64.93(1 − x) = 63.55
2.00x = 1.38 → x = 0.690 → 69.0% Cu-63 and 31.0% Cu-65
For a two-isotope problem, set the abundances to x and 1 − x and solve the single linear equation.
Isotopes are atoms of the same element with different numbers of neutrons: identical atomic numbers, different mass numbers. Isotopes have nearly identical chemical properties because chemical behavior depends on electron configuration, which is set by the atomic number. They differ in mass-dependent physical properties (density, rate of diffusion) and in nuclear stability.
Notation
Isotopes are written as element–mass number (carbon-12, C-12) or in symbolic notation with the mass number as a left superscript and the atomic number as a left subscript: carbon-12 is ¹²₆C and carbon-14 is ¹⁴₆C. Both carbon isotopes have 6 protons; C-12 has 6 neutrons and C-14 has 8.
Stable and Unstable Isotopes
Stable isotopes do not undergo radioactive decay. Unstable isotopes (radioisotopes) spontaneously emit radiation to reach a more stable nucleus. Stability depends on the neutron-to-proton ratio: light elements are most stable with approximately equal numbers of protons and neutrons (n/p ≈ 1), while heavier elements require more neutrons than protons (n/p approaching 1.5 for the heaviest stable nuclei).
| Isotope | Protons | Neutrons | Notes |
|---|---|---|---|
| Protium ¹H , | 1 | 0 | Mostabundanthydrogenisotope |
| Deuterium ²H(D) , | 1 | 1 | Stable; used in heavy water D ₂O , |
| Tritium ³H(T) , | 1 | 2 | Radioactive |
| Carbon-12 | 6 | 6 | 989%ofnaturalcarbon;definestheamu(exactly12amu) . |
| Carbon-13 | 6 | 7 | 11%ofnaturalcarbon;stable . |
| Carbon-14 | 6 | 8 | Traceamounts;radioactive;usedinradiocarbondating |
Applications
Radiocarbon dating: carbon-14 dates organic materials up to approximately 50,000 years old.
Medical imaging: radioisotopes such as technetium-99m are used as diagnostic tracers.
Nuclear power: uranium-235 and plutonium-239 undergo fission in reactors.
Research: isotope labeling (for example, ¹⁸O or ¹³C) traces atoms through reaction pathways.
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